Active resistor-capacitor (RC) integration and switched-capacitor integration are both commonly used to process incoming signals in data transmission networks. Each of these integration functions is commonly implemented, in part, using an amplifier with capacitive feedback to perform the integration. One common type of amplifier that is used in such circuits is a transconductance amplifier.
In operation, a transconductance amplifier outputs a current proportional to its input voltage, i.e.,IOUT=GM·VIN  (1)
where VIN is the input voltage of the amplifier, IOUT is the output current of the amplifier, and GM is the transconductance of the amplifier.
The transconductance amplifier thus receives the input voltage VIN and then supplies the output current IOUT in proportion to the amplifier's transconductance GM. This means that if the input voltage VIN remains relatively stable, the higher the required output current IOUT, the higher the required transconductance GM for the amplifier.
Ideally, a transconductance amplifier will have zero input current IIN, though practically, the input current IIN is simply very small. This small input current IIN passing over the input impedance of the transconductance amplifier can provide the input voltage VIN. Similarly, an output voltage VOUT can be obtained by passing the output current IOUT over the output impedance of the transconductance amplifier.
During operation, active-RC integrators and switched-capacitor integrators each impose different amplifier performance criterion on a transconductance amplifier. As a result, where the same transconductance amplifier is used in both active-RC integrator and switched-capacitor integrator circuits, there can be a requirement for a very large transconductance. This is particularly true when a large signal-to-noise-plus-distortion ratio (SNDR) is required for a signal passing through the amplifier.
The signal-to-noise ratio (SNR) of an incoming signal generally indicates the ratio of the received signal power of the incoming signal to the noise power of the incoming signal. It is useful as an indicator of the reliability of the incoming signal. The SNDR for an incoming signal is similar, but indicates the ratio of the signal power of the incoming signal to the received noise-plus-distortion power of the incoming signal. This can be a more useful indicator of the reliability of the incoming signal in cases where distortion is common, such as in modulated audio signals in which distortion can result from a carrier radio frequency.
Increasing the transconductance GM of a transconductance amplifier can be expensive in terms of money and die space, however. This is particularly true in a CMOS device, for example, which is a commonly-used implementation for amplifiers. One reason for this is that the transconductance GM of a CMOS amplifier improves in accordance with the square root of the width of the amplifier, i.e.,GM∝√{square root over (W)}  (2)
where W is the width of the amplifier. Since amplifier width and current passing through are related, this can be extended to say that the transconductance GM of the CMOS device rises in accordance with the square root of the current passing through the amplifier, i.e.,GM∝√{square root over (IA)}  (3)
where IA is the current passing through the amplifier.
As a greater output current IOUT is required for the amplifier, a correspondingly greater current IA is required to pass through the amplifier, necessitating an increase in the transconductance GM of the amplifier. Since space on a CMOS device is extremely valuable, increasing W can significantly increase the cost of the resulting device, or at the very least, decrease the amount of other circuitry allowed to be included in the resulting device. And increasing the amplifier current IA means greater power consumption, which can increase the battery drain in a portable device.